Regex how to match all end of line except empty line?

If I have text:

AAAAAA
BBBBBB
CCCCCC

DDDDDD
EEEEEE

FFFFFF
GGGGGG
HHHHHH

      

        
        
        
      

    

I want to match the entire end of the line except empty lines and replace the end of the line with a tab. [^\s]$

partially works, but also matches the last character of a nonblank string. [^^]$

does not work. What's the correct regular expression?